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Re: st: Modelling two binary outcomes that are not mutually exclusive

From   Joseph Coveney <>
To   Statalist <>
Subject   Re: st: Modelling two binary outcomes that are not mutually exclusive
Date   Sun, 28 Nov 2004 01:31:11 +0900

Ronán Conroy wrote:

I have two binary outcomes, measured in a patient population (anxiety 
and depression). For various reasons, I suspect that a number of patient 
characteristics predict depression but not anxiety.

If the two diagnoses were mutually exclusive, all would be well. I could 
use multinomial logistic regression and compare the coefficients. 
However, there is about a 20% overlap. Is this a Known Problem? I could 
model the overlap category as a third outcome, and show that the 
coefficients were similar to those for depression alone and different to 
those for anxiety alone, but this is slicing the sample a little thin - 
there are just 8 people with both disorders. (This approach actually 
works, sort of, given the small numbers, so I'm on the right track from 
the theory point of view.)

Any suggestions out there?


Would -biprobit- (along the lines of Mark Schaffer's suggestion), or -xtprobit- 
lend any help?

As an alternative, would formally modeling as a bivariate binomial regression 
using -gllamm- (two random effects, one for each outcome, ŕ la Van 
Houwelingen's bivariate approach to meta-analysis) help?

Joseph Coveney

set more off
drawnorm y1 x1 x2, mean(0 0 0) ///
  sd(1 1 1) corr(1 0.7 0.7 \ 0.7 1 0.7 \ 0.7 0.7 1) ///
  n(200) seed(`=date("2004-11-28", "ymd")')
generate byte y0 = uniform() > 0.5 // y0, Anxiety
replace y1 = y1 > 0  // y1, Depression
biprobit y0 y1 x1 x2
// It shows that y1 is predicted and not y0
generate int pid = _n
reshape long y, i(pid) j(dep)
xi: xtprobit y i.dep*x1 i.dep*x2, i(pid) re
// The dependent-variable-by-predictor interaction terms 
// indicate that one is predicted and not the other (given the
// necessary assumptions)

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